Clipping is a common type of distortion in which the amplitude of a signal is truncated if it exceeds a certain threshold. Sparse representation has underpinned several algorithms developed recently for reconstruction of the original signal from clipped observations. However, these declipping algorithms are often built on a synthesis model, where the signal is represented by a dictionary weighted by sparse coding coefficients. In contrast to these works, we propose a sparse analysis-model-based declipping (SAD) method, where the declipping model is formulated on an analysis (i.e. transform) dictionary, and additional constraints characterizing the clipping process. The analysis dictionary is updated using the Analysis SimCO algorithm, and the signal is recovered by using a least-squares based method or a projected gradient descent method, incorporating the observable signal set. Numerical experiments on speech and music are used to demonstrate improved performance in signal to distortion ratio (SDR) compared to recent state-of-the-art methods including A-SPADE and ConsDL.

中文翻译：

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基于稀疏分析模型的字典学习的信号去噪

削波是失真的一种常见类型，其中，如果信号的幅度超过某个阈值，则该信号的幅度将被截断。稀疏表示法支持最近开发的几种算法，这些算法可用于从限幅观测中重建原始信号。但是，这些去噪算法通常建立在合成模型上，其中信号由稀疏编码系数加权的字典表示。与这些工作相反，我们提出了一种基于稀疏分析模型的减幅（SAD）方法，其中，减幅模型是基于分析（即变换）字典制定的，并附加了表征削波过程的约束条件。使用Analysis SimCO算法更新分析字典，并使用基于最小二乘法的方法或投影梯度下降方法恢复信号，合并可观察的信号集。与最近的最新技术（包括A-SPADE和ConsDL）相比，语音和音乐的数值实验用于证明信噪比（SDR）的改进性能。